The Red Devils' shock exit from the Champions League at the hands of Sevilla on Tuesday night means that the FA Cup remains the side's sole chance at silverware this season, with only the runners-up spot up for grabs in the league.
Speaking after the Champions League exit, Mourinho claimed that the defeat was "nothing new" for United and also referenced previous times that he had ousted the club from the competition as an opposition manager.
Mourinho is also alleged to have not admonished his players after the game, instead visiting the Sevilla dressing room to congratulate them.
According to the Daily Mail, Mourinho's demeanour coupled with United's results and performances this season have left some boardroom members "uncomfortable" with the club's direction of travel.
The newspaper says that senior figures are concerned by "the style of football being played by the Portuguese coach and fear that it could be several years before his team are serious contenders for the Premier League title".
One senior source is quoted as saying: "Jose is not the manager we thought he was. We are worried. We know the fans hate the football, and we won't win the league for three or four years. He's also too insecure and gets involved in things away from the football."
United executive vice-chairman Ed Woodward is thought to have given his full backing to Mourinho, who has spent more than £300m during his time in charge at Old Trafford.